If physics is an information science, what is an observer?

Interpretations of quantum theory have traditionally assumed a "Galilean" observer, a bare "point of view" implemented physically by a quantum system. This paper investigates the consequences of replacing such an informationally-impoverished observer with an observer that satisfies the requirements of classical automata theory, i.e. an observer that encodes sufficient prior information to identify the system being observed and recognize its acceptable states. It shows that with reasonable assumptions about the physical dynamics of information channels, the observations recorded by such an observer will display the typical characteristics predicted by quantum theory, without requiring any specific assumptions about the observer's physical implementation.Comment: 30 pages, comments welcome; v2 significant revisions - results unchange

Composable consistency for large-scale peer replication

technical reportThe lack of a flexible consistency management solution hinders P2P implementation of applications involving updates, such as directory services, online auctions and collaboration. Managing shared data in a P2P setting requires a consistency solution that can operate in a heterogenous network, support pervasive replication for scaling, and give peers autonomy to tune consistency to their sharing needs and resource constraints. Existing solutions lack one or more of these features. In this paper, we propose a new way to structure consistency management for P2P sharing of mutable data called composable consistency. It lets applications compose a rich variety of consistency solutions appropriate for their sharing needs, out of a small set of primitive options. Our approach splits consistency management into design choices along five orthogonal aspects, namely, concurrency, consistency, availability, update visibility and isolation. Various combinations of these choices can be employed to yield numerous consistency semantics and to fine-tune resource use at each replica. Our experience with a prototype implementation suggests that composable consistency can effectively support diverse P2P applications

Multilinear Superhedging of Lookback Options

In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $\theta(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their (zero-sum) game has the payoff kernel $W_\theta(X)/D(X)$, where $W_\theta(X)$ is the trader's final wealth and $D(X)$ is the final wealth that would have accrued to a $\$1$ deposit into the best constant-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. The resulting "universal portfolio" compounds its money at the same asymptotic rate as the best rebalancing rule in hindsight, thereby beating the market asymptotically under extremely general conditions. Smitten with this (1998) result, the present paper solves the most general tractable version of Cover and Ordentlich's (1998) max-min game. This obtains for performance benchmarks (read: derivatives) that are separately convex and homogeneous in each period's gross-return vector. For completely arbitrary (even non-measurable) performance benchmarks, we show how the axiom of choice can be used to "find" an exact maximin strategy for the trader.Comment: 41 pages, 3 figure